Answer:
56.75% probability that a mechanic can complete 16 oil changes in an eight-hour day
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What is the probability that a mechanic can complete 16 oil changes in an eight-hour day
16 oil changes in 8 hours is 2 changes per hour, that is, one each 30 minutes.
This probability is the pvalue of Z when X = 30. So
has a pvalue of 0.5675
56.75% probability that a mechanic can complete 16 oil changes in an eight-hour day